Stereotactic Brain Microanatomy
Stereotactic brain anatomy is the study of brain anatomy using a three-dimensional coordinate system. It deals with precise identification and localization of brain structures and distances in space in order to serve to neurosurgery. There are several stereotactic atlases of the human brain. The precision of some of them are submillimetric.
This book introduces the topic focusing on the details of the mathematical basis of stereotactic brain anatomy. A three-dimensional coordinate system is placed with the origin in the MCP (midcommissural point). The axis $z$ points upwards, the axis $x$ points from the right to the left cerebral hemisphere, and the axis $y$ points from AC (anterior commissure) to PC (posterior commissure). An extensive explanation of how to locate these points is given.
The first 4 chapters introduce mathematical features, which are linear algebra facts for three-dimensional
space (cartesian coordinates, lines, planes, distances, etc), and then moves to the application to stereotactic. For instance, planar sections of the brain are sagital if parallel to the $yz$ plane, coronal if parallel to the $xz$ plane, and transverse if parallel to the $xy$ plane. Chapter 5 introduces changes of coordinates by translation and rotation, and also other sets of coordinates, mainly cylindrical and spherical. Applications to locating points in the brain for neurosurgery are reviewed. The last two chapters explain how the stereotactic atlases are produced, by locating different areas of the brain by coordinatizing the regions (via inequalities on the coordinate functions). Every chapter ends with a summary of the issues explained, putting them in relation to mathematical language.
The book can be helpful to students in medicine and to neuroscientists who want to learn the mathematical facts behind. The mathematics are elementary, but as remarked in the book they are often used mistakenly. The book can be interesting to mathematicians who want to learn applications to real life, and may serve for teaching on applications of linear algebra to undergraduate students in mathematics, biology, and science in general.